How to properly render a curve/thin object in Cycles?
Two setting for the curve you need to change, to change the curve's resolution.

First to add more loops along the length of the curve change the Resolution of the curve.
The Preview setting controls the amount of loops displayed in the 3D view. The Render setting controls how many get rendered, if it is set to 0, then the Preview number is used.

To add more points around the circumference of the curve change the Resolution of the Bevel.